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Trudy Inst. Mat. i Mekh. UrO RAN, 2021, Volume 27, Number 3, Pages 271–285 (Mi timm1856)  

Wilcox Formula for Vector Fields on Banach Manifolds

Yuri S. Ledyaevab

a Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
b Western Michigan University

Abstract: We obtain an analogue of Wilcox-Snyder formula for flows of diffeomorphisms of $C^m$-smooth vector fields on infinite-dimensional Banach manifolds. For classical linear system this formula can be efficiently used, for example, to obtain Magnus expansion of solutions. The generalized Wilcox formula is obtained by using an extended Chronological Calculus for Banach manifold. We apply this formula to derive new structured differential equations which solutions approximate solutions of the original differential equation.

Keywords: flow of diffeomorphisms, Wilcox formula, chronological calculus, Magnus expansion.

DOI: https://doi.org/10.21538/0134-4889-2021-27-3-271-285

Full text: PDF file (212 kB)
First page: PDF file
References: PDF file   HTML file

MSC: 93C10, 45G15
Received: 20.07.2021
Revised: 11.08.2021
Accepted:23.08.2021
Language:

Citation: Yuri S. Ledyaev, “Wilcox Formula for Vector Fields on Banach Manifolds”, Trudy Inst. Mat. i Mekh. UrO RAN, 27, no. 3, 2021, 271–285

Citation in format AMSBIB
\Bibitem{Led21}
\by Yuri~S.~Ledyaev
\paper Wilcox Formula for Vector Fields on Banach Manifolds
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2021
\vol 27
\issue 3
\pages 271--285
\mathnet{http://mi.mathnet.ru/timm1856}
\crossref{https://doi.org/10.21538/0134-4889-2021-27-3-271-285}
\elib{https://elibrary.ru/item.asp?id=46502708}


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